Can someone pls pls pls help me with this questions asap! Thanks so much

Edgar

Let L = C(s,t) where s and t are indeterminates (or more formally L is the field of fractions of C[s,t]). Let Φ: L → L be given by Φ(s) = t, Φ(t) = s, and let G be the group generated by Φ. Find the fixed field of G, justifying your answer.

Feb 24th 2008, 09:24 PM

ThePerfectHacker

Quote:

Originally Posted by edgar davids

Let L = C(s,t) where s and t are indeterminates (or more formally L is the field of fractions of C[s,t]). Let Φ: L → L be given by Φ(s) = t, Φ(t) = s, and let G be the group generated by Φ. Find the fixed field of G, justifying your answer.

I never studied anything about these types of problems before so this is just a guess.

Say that,
.... .

It must have this form because, it cannot be that degree of t exceedes degree of s for that would make the polynomial of degree s exceedes degree of t which means it cannot be the same after applying the automorphism to it.

Now this value stays unchanged under . The values across the diagnols can be anything while .